With the widespread of telecommunication services coupled with the introduction of various multimedia and high quality services, demands for communication services are increasing rapidly. In wireless communication systems, frequency resources are limited and shared with other users. In order to actively respond to the demands, the capacity of the communication system plays an important role. As such, it is important to discover available frequency bandwidth and/or improve efficiency in using existing frequency resources. To address this limited frequency resources problem, researches related to spatial-time domain encoding are taking place to improve wireless resource efficiency. For example, researches related to systems having multiple antennas both at the transmitting and the receiving sides are actively being researched so that communication reliability can be increased using existing resources through diversity gain and/or using parallel transmissions to increase transmission capacity.
FIG. 1 illustrates a structural diagram of a communication device for transmission/reception. More specifically in FIG. 1, the transmitting end includes a channel encoder 101, a mapper 102, a serial/parallel (S/P) converter 103, a multiple antenna encoder 104, and multiple transmit antennas 105.
The channel encoder 101 reduces noise effect by adding repeated bits (e.g., cyclic redundancy bits) to the data bits. The mapper 102 performs constellation mapping where the data bits are allocated/mapped into data symbols. The S/P converter 103 converts serially inputted data into parallel data. The multiple antenna encoder 104 encodes the data symbols into time-space signals. The multiple antennas 105 transmit the time-space encoded signals to a plurality of channels.
The receiving end includes multiple receiving antennas 106, a multiple antenna decoder 107, a parallel/serial (P/S) converter 108, a demapper 109, and a channel decoder 110. The multiple receiving antennas 106 receive signals via the plurality of channels. The multiple antenna decoder 107 decodes time-space signals encoded by the multiple antenna encoder 104 and converts the decoded signals into data symbols. Further, the P/S converter 108 converts the parallel symbols into serial symbols. The demapper 109 converts the serial data symbols to bits. Lastly, the channel decoder decodes the channel codes processed through channel encoder 101 and then estimates the data.
As discussed above, the multiple antenna encoder 104 performs space-time coding. Table 1 shows space-time codes derived from two or four transmit antennas.
TABLE 1Numberdp.min (minimumofRankproduct distance)SchemeRateAntennas(Tx)(QPSK)(1)      1          2        ⁡      [                                        S            1                                                -                          S              2              *                                                                        S            2                                                S            1                                ]  1211 (2)      1          2        ⁡      [                                        S            1                                                            S            2                                ]  2211 (3)            1                        2          ⁢                      (                          1              +                              r                2                                      )                                ⁡          [                                                                  S                1                            +                              jr                ·                                  S                  4                                                                                                        r                ·                                  S                  2                                            +                              S                3                                                                                                        S                2                            -                              r                ·                                  S                  3                                                                                                        jr                ·                                  S                  1                                            +                              S                4                                                        ]        ,      r    =                  5            ±              1        2            2220.2 (4)      1    2    ⁡      [                                        S            1                                                S            2                                                S            3                                                S            4                                                            S            2            *                                                -                          S              1              *                                                            S            4            *                                                -                          S              3              *                                                                        S            3                                                -                          S              4                                                            -                          S              1                                                            S            2                                                            S            4            *                                                S            3            *                                                -                          S              2              *                                                            -                          S              1              *                                            ]  1424 (5)      1          2        ⁡      [                                        S            1                                                S            2                                    0                          0                                                  -                          S              2              *                                                            S            1            *                                    0                          0                                      0                          0                                      S            3                                                S            4                                                0                          0                                      -                          S              3              *                                                            S            3            *                                ]  1421 (6)      1    2    ⁡      [                                        S            1                                                -                          S              2              *                                                            S            5                                                S            6                                                            S            2            *                                                S            1            *                                                S            6                                                S            5            *                                                            S            3                                                -                          S              4              *                                                            S            7                                                -                          S              8              *                                                                        S            4                                                S            3            *                                                S            8                                                S            7            *                                ]  2421
The space-time codes of Table 1, namely, (1), (2), and (3), are space-time codes related to two (2) transmit antennas whereas (4), (5), and (6) are space-time codes related to four (4) transmit antennas.
The use of multiple antennas was proposed for the purposes of increasing capacity, throughput, and/or coverage of the wireless communication system. The multiple antennas are used to employ schemes such as a spatial division multiplexing (SDM or SM) and a space-time coding (STC). More specifically, the SM scheme sends different data to each of the multiple antennas so as to maximize the transmission rate. Further, the STC scheme encodes the symbols across the spatial domain (e.g., antennas) and the time domain to attain diversity gain as well as coding gain so as to increase link level capability. In addition, a generalized form of the combination of SM and STC schemes is a linear dispersion coding (LDC). The LDC matrix can be used in encoding/decoding operations of the multiple antennas, and at the same time, in representing various techniques of the multiple antennas.
The multiple antenna encoding technique according to the LDC matrix can be represented by the following equation.
                    S        =                              ∑                          q              =              1                        Q                    ⁢                                    S              q                        ⁢                          M              q                                                          [                  Equation          ⁢                                          ⁢          1                ]            
In Equation 1, Q denotes a number of data transmitted during a LDC interval, T denotes the LDC interval, Sq denotes qth transmission data and Sq=αq+j*βq, Mq denotes is a dispersion matrix, having a size of T×Nt, which is multiplied to the qth transmission data, and S denotes a transmission matrix. Here, ith column of the S transmission matrix represents symbols that are transmitted during the ith time period or time slot, and jth row represents symbols that are transmitted by the jth antenna.
More generally, if each of an actual part (αq) and an imaginary part (βq) of Sq is spread across the space-time plane by different dispersion matrix, this can be represented by Equation 2.
                    S        =                              ∑                          q              =              1                        Q                    ⁢                      (                                                            α                  q                                ⁢                                  A                  q                                            +                              j                ⁢                                                                  ⁢                                  β                  q                                ⁢                                  B                  q                                                      )                                              [                  Equation          ⁢                                          ⁢          2                ]            
In Equation 2, Aq and Bq each denotes a dispersion matrix, having a size of T×Nt, which is respectively multiplied to the actual part and the imaginary part of Sq.
If the data symbols are transmitted via the transmit antennas according to the scheme(s) as described above, the receiving signals received by the receiving antennas can be expressed as follows. If the receiving signals are multiplied to Sq by the same or identical LDC matrix, then it can be expressed according to the following equation.
                              [                                                                      Y                  1                                                                                    ⋮                                                                                      Y                  Nr                                                              ]                =                              H            ⁢                                                  ⁢                          χ              ⁡                              [                                                                                                    S                        1                                                                                                                        ⋮                                                                                                                          S                        Q                                                                                            ]                                              +                      [                                                                                n                    1                                                                                                ⋮                                                                                                  n                    Nr                                                                        ]                                              [                  Equation          ⁢                                          ⁢          3                ]            
An equivalent channel response can be expressed by Equation 4 if the LDC, as shown in Equation 1, is applied.H=Ir{circle around (x)}H, χ=[vec(M0)vec(M1) . . . vec(MQ)]  [Equation 4]
In Equations 3 and 4, Nr denotes a number of receiving antennas, yNr denotes a signal value of the Nrth receiving antenna, nNr denotes noise from the Nrth receiving antenna, H denotes the equivalent channel response, and H denotes a channel response matrix having a size of Nr×Nt.
If the receiving signal is applied the LDC of Equation 2, then the receiving signal can be expressed as follows.
                              [                                                                      Y                                      R                    ,                    1                                                                                                                        Y                                      I                    ,                    1                                                                                                      ⋮                                                                                      Y                                      R                    ,                    Nr                                                                                                                        Y                                      I                    ,                    Nr                                                                                ]                =                              H            ⁡                          [                                                                                          α                      1                                                                                                                                  β                      1                                                                                                            ⋮                                                                                                              α                      Q                                                                                                                                  β                      Q                                                                                  ]                                +                      [                                                                                n                                          R                      ,                      1                                                                                                                                        n                                          I                      ,                      1                                                                                                                    ⋮                                                                                                  n                                          R                      ,                      Nr                                                                                                                                        n                                          I                      ,                      Nr                                                                                            ]                                              [                  Equation          ⁢                                          ⁢          5                ]            
In Equation 5, R (subscript) denotes the real part of the signal, and I (subscript) denotes the imaginary part of the signal. Here, the equivalent channel response can be expressed as shown in Equation 6.
                              H          ⁡                      [                                                                                                      A                      1                                        ⁢                                                                  h                        _                                            1                                                                                                                                  B                      1                                        ⁢                                                                  h                        _                                            1                                                                                        …                                                                                                                    A                        Q                                            1                                        ⁢                                                                  h                        _                                            1                                                                                                                                  B                      1                                        ⁢                                                                  h                        _                                            1                                                                                                                    ⋮                                                  ⋮                                                  ⋱                                                  ⋮                                                  ⋮                                                                                                                        A                      1                                        ⁢                                                                  h                        _                                            Nr                                                                                                                                  B                      1                                        ⁢                                                                  h                        _                                            Nr                                                                                        …                                                                                            A                      Q                                        ⁢                                                                  h                        _                                            Nr                                                                                                                                  B                      Q                                        ⁢                                                                  h                        _                                            Nr                                                                                            ]                          ,                                  ⁢                              A            q                    =                      [                                                                                A                                          R                      ,                      q                                                                                                            -                                          A                                              I                        ,                        q                                                                                                                                                              A                                          I                      ,                      q                                                                                                            A                                          R                      ,                      q                                                                                            ]                          ,                                  ⁢                              B            q                    =                      [                                                                                -                                          B                                              I                        ,                        q                                                                                                                                  -                                          B                                              R                        ,                        q                                                                                                                                                              B                                          R                      ,                      q                                                                                                            -                                          B                                              I                        ,                        q                                                                                                                  ]                          ,                                  ⁢                              h            n                    =                      [                                                                                h                                          R                      ,                      n                                                                                                                                        h                                          I                      ,                      n                                                                                            ]                                              [                  Equation          ⁢                                          ⁢          6                ]            
In Equation 6, hR,n denotes the real parts of the channel response vector received via nth receiving antenna, and h\I,n denotes the imaginary parts of the channel response vector received via nth receiving antenna. In other words, the multiple antenna decoding is a process by which transmitted signals are decoded using equations such as Equation 3 or Equation 5. To put differently, the multiple antenna decoding is a process of estimating Sq or αq and βq.
In addressing capacity problems, a multiple input multiple output (MIMO) can be used increase transmission capacity of the wireless communication system. Further, a space-time block coding, proposed by Alamouti, (A Simple Transmit Diversity Technique for Wireless Communications, IEEE JSAC, vol. 16, no. 8, October 1998) is an exemplary transmit diversity technique which uses a plurality of transmitting/receiving antennas to overcome fading in wireless channels. The Alamouti proposed scheme uses two (2) transmit antennas, and the diversity order equals a product of a number of transmit antennas and a number of receiving antennas. Here, the Alamouti proposed scheme transmits two (2) data symbols during two (2) time slots via two (2) transmit antennas, and as a result, a transmit rate (spatial multiplexing rate) is only 1. Consequently, the spatial multiplexing gain cannot be attained regardless how many receiving antennas are available. Here, the Alamouti proposed scheme does not discuss the transmit techniques associated with three (3) or more transmit antennas.
In addition, Bell Laboratories introduced another spatial multiplexing technique known as a vertical bell laboratories layered space-time (V-BLAST) system (Detection Algorithm and Initial Laboratory Results Using V-BLAST Space-Time Communication Architecture, IEEE, Vol. 35, No. 1, pp. 14-16, 1999). In this technique, each transmit antenna transmits independent signals simultaneously using the same transmit power and rate. At the receiving end, the transmitted signals are processed through detection ordering, interference nulling, and interference cancellation procedures. By using the V-BLAST system, unnecessary interference signals can be eliminated or reduced thus increasing a signal-to-noise ratio (SNR). This technique is useful if the number of receiving antennas is equal or greater than the number of transmit antennas since independent data signals, corresponding to the number of transmit antennas, can be simultaneously transmitted attaining a maximum spatial multiplexing gain. Here, a possible drawback is that there has to be more receiving antennas than the transmit antennas. Moreover, if the channel condition is bad and thus the received signal is unsuccessfully decoded, detecting and decoding subsequent signal is likely to be affected as well affecting the system performance.
Further, different from the two techniques discussed above, Yao and Wornwell (hereafter, “Yao”) proposed another spatial multiplexing technique called tilted-quadrature amplitude multiplexing (QAM) (Structured Space-Time Block Codes with Optimal Diversity-Multiplexing Tradeoff and Minimum Delay, Globecom, pp. 1941-1945, 2003). This technique is a full diversity and full rate (FDFR) STC which complements an optimal diversity-multiplexing tradeoff proposed by Zheng and Tse. Yao's technique is used in a system having two (2) transmit antennas and two (2) receiving antennas where a short space-time block code has a minimum code length of 2. Further, the technique employs QAM constellation rotation to attain spatial multiplexing gain as well as full diversity gain. However, shortcomings with this technique is that coding gain is not fully realized since the rotation is a simple rotation of the signal, and the technique is applied and limited to systems having two (2) transmit and receiving antennas, respectively.